If the data doesn't change very much, have you considered a file sync
solution, possibly with versioning if needed, rather than a traditional file backup
solution? That would alleviate the risk of a relatively small bit of corruption potentially wiping out your entire backup, since a sync solution keeps your files as independent files at the replication destination. And version control would allow you to maintain some form of history.
If you want to use Reflect though, then my first question is how large your weekly backups are. If they're not very frequent, you might want to consider changing your schedule to run every 8 weeks, or every 12 weeks, for example. Weekly backups allow you to specify that they should only run every X weeks -- though monthly backups also allow you to choose to have them run only on certain months, I suppose. As far as the integrity check goes, if you run backups rather infrequently, you could simply do that manually. By default, choosing to verify a Diff or Incremental will verify the preceding/parent backup(s) that it depends on, unless you specifically choose to verify only that file. However, the auto-verify feature you can configure does NOT do that; it only verifies the backup that was just created. You could even potentially script something if you wanted, since Reflect has a verification utility that can be used from the command line, as documented here